From Moscow's Kursky vokzal (station) express trains "Lastochka" or "Strizh" leave at 07:15,09:30,11:00, 14:15, 16:45 and 18:30 to Vladimir, the price of a ticket is around 500 - 1100Rbl. (tickets here pass.rzd.ru).The journey to Vladimir takes about 2 hours.
At Vladimir you need to cross over to the bus station and buy a ticket (approx 110Rbl) for the bus to Suzdal (journey time is around 50 minutes), which leaves every half an hour from 06:30 until 21:40. The bus will take you to the bus station at the edge of Suzdal and there you can take another bus or a taxi that will take you into the centre (the centre of Suzdal is approximately a 40 minute walk from the bus station).
Alternatively you can get to Suzdal by one of the buses that leave from the Moscow Central bus station (metro Shchelkovskaya). The price for the bus is about 550Rbl and the buses tend to leave every hour or so, depending on when the driver has decided that the bus is full enough to set off. Be sure to check that your bus is heading to Suzdal as there are many buses here that also head off to completely different Russian cities too. The bus usually makes one toilet stop on route and the journey can take about between 4 and 4.5 hours depending on traffic.
The cost of travel in any municipal transport: 19Rbl.